The way my CP explained it is this: Both pilots and cops typically work long hours, have strange sleep schedules, and eat meals at "off" times. We both have large responsibility, and don't receive much recognition for a job well done (we have to appreciate ourselves for what we do). When things are going well, it's somewhat mundane, yet when things start going wrong, it gets challenging, exciting, scary, etc./all of the above.
Both groups work without their boss right over their shoulder (obviously cops deal with their sergeants more), and try to stay out of the chief's office. Both groups have to try and keep their opinions to themselves (no talking to the media, and watch what you say online), and typically keep circles of friends who are also cops/pilots. Get pilots or cops in a group, and we speak our own language... "There I was on the ILS, shooting it down to 1800 RVR with an 18-knot crosswind, when we lose the glideslope and have to go-around and divert..." or "so I'm 10-97 on the TC, and step out of the squad only to trip and watch in horror as my BUG falls right onto the pavement..."
My boss said being in LE will be more physically demanding, in terms of possible injury, or day-to-day bumps and bruises, but he feels that LE offers a better quality of life, considering you'll have a semi-regular schedule and be home every night. He did say, by far, that LE blows aviation away in terms of benefits and retirement. Even medium-sized municipalities have better benefits that the regionals, and federal/state LEOs have much better retirement and benefits than most major airlines.
The way I see it, it's just a roll of the dice. Aviation could improve, and those of us who don't stick with it will be kicking ourselves that we left the industry. Or, things will continue to deteriorate, and soon we'll all be too old to pursue law enforcement. I have a friend who now is too old to change into a LE career, and an injury from this job prevents him from being a cop even if he was under the maximum age. It's sad, because he wants out.
In the end, whatever I do, I just want to end the day and feel like I've served, and I want to feel good about what I do. Then I want to go home and see my family, and be a big part of my kids growing up.